1. No category

Guillem Perarnau
School of Computer Science (McGill University) ◇ Office 311, McConnell Building ◇
845 Sherbrooke Street West, Montreal (QC), Canada, H3A 0G4
H(514) 655-5992 ◇ B p.melliug@gmail.com ◇ http://cgi.cs.mcgill.ca/~guillem/
POSITION
Since October 2013, I am a Postdoctoral researcher at McGill University.
RESEARCH INTERESTS
Probabilistic and Extremal Combinatorics, Random Combinatorial Structures, Graph Colorings,
Randomized Algorithm Analysis.
EDUCATION
PhD in Applied Mathematics
Department of Applied Mathematics IV (UPC-BarcelonaTech).
2010 – 2013
Barcelona, Spain
Thesis dissertation: Random Combinatorial Structures with low dependencies: existence and
enumeration (click here to download it). Supervised by Oriol Serra.
Master’s degree in Applied Mathematics
School of Mathematics and Statistics (UPC-Barcelona Tech).
2009 – 2010
Barcelona, Spain
Bachelor’s degree in mathematics
School of Mathematics and Statistics (UPC-Barcelona Tech).
2004 – 2009
Barcelona, Spain
FELLOWSHIPS AND AWARDS
FPU PhD fellowship from the Spanish Ministry of Science
2011 – 2013
FPI-UPC PhD fellowship from the UPC-BarcelonaTECH
2009– 2011
CERMET Scholarship
2009
Scholarship for undergraduate research
2008
JOURNAL PUBLICATIONS
Forthcoming
● F. Joos, G. Perarnau, D. Rautenbach and B. Reed. The giant component in random graphs
with given degree sequence. In preparation.
● G. Chapuy and G. Perarnau. Connectivity in bridge-addable graph classes: the McDiarmidSteger-Welsh conjecture. Submitted. ArXiv Preprint
● L. Addario-Berry, B. Balle and G. Perarnau. Diameter and Stationary Distribution of Random
r-out Digraphs. Submitted. ArXiv Preprint
● N. Bousquet and G. Perarnau. Fast Recoloring of Sparse Graphs. Submitted. ArXiv Preprint.
● X.S. Cai, G. Perarnau, B. Reed and A.B. Watts. Acyclic edge colourings of graphs with large
girth. Submitted. ArXiv Preprint.
Last updated: May 1, 2015
Guillem Perarnau, Page 1 of 6
● G. Perarnau and O. Serra. Correlation among runners and some results on the Lonely Runner
Conjecture. Submitted. ArXiv Preprint.
● G. Perarnau and B. Reed. Existence of spanning F-free subgraphs with large minimum degree.
Submitted. ArXiv Preprint.
● J. Diaz, D. Mitsche, G. Perarnau and X. P´erez-Gim´enez. On the relation between graph
distance and Euclidean distance in random geometric graphs. Submitted. ArXiv Preprint.
● F. Foucaud, G. Perarnau and O. Serra. Random subgraphs make identification affordable.
Submitted. ArXiv Preprint.
● D. Mitsche and G. Perarnau. On the treewidth and related parameters of random geometric
graphs. Submitted.
Published
● F. Foucaud, M. Krivelevich and G. Perarnau. Large subgraphs without short cycles. SIAM
Journal of Discrete Mathematics 29(1):65-78, 2015. ArXiv Preprint.
● R. Kang and G. Perarnau. Decomposition of bounded degree graphs into C4 -free subgraphs,
European Journal of Combinatorics, 44(A):99-105, 2015. ArXiv Preprint.
● A. Abiad, M.A. Fiol, W.H. Haemers and G. Perarnau. An interlacing approach for bounding
the sum of laplacian eigenvalues of graphs, Linear Algebra and its Applications, 448:1121,
2014. ArXiv Preprint.
● G. Perarnau and O. Serra. On the tree-depth of random graphs, Discrete Applied Mathematics,
168:119-126, 2014. ArXiv Preprint.
● G. Perarnau and O. Serra. Rainbow Perfect Matchings in Complete Bipartite Graphs: Existence and Counting, Combinatorics, Probability and Computing, 22(5):783-799, 2013. ArXiv
Preprint.
● G. Perarnau. A probabilistic approach to consecutive pattern avoiding in permutations, Journal
of Combinatorial Theory, Series A, 120(5):998-1011, 2013. ArXiv Preprint.
● G. Perarnau and G. Petridis. Matchings in Random Biregular Bipartite Graphs, The Electronic Journal of Combinatorics 20(1):P60, 2013. ArXiv Preprint.
● F. Foucaud, I. Honkala, T. Laihonen, A. Parreau and G. Perarnau. Locally identifying colourings for graphs with given maximum degree, Discrete Mathematics, 312(10):1832-1837, 2012.
ArXiv Preprint.
● F. Foucaud and G. Perarnau. Bounds for identifying codes in terms of degree parameters,
The Electronic Journal of Combinatorics 19(1):P32, 2012. ArXiv Preprint.
CONFERENCE PUBLICATIONS
● F. Foucaud, G. Perarnau and O. Serra. Random subgraphs make identification affordable,The
Seventh European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB 2013) CRM Series Volume 16, pp 415-420. Pisa, Italy, 2013.
● A. Abiad, M.A. Fiol, W.H. Haemers and G. Perarnau. An interlacing approach for bounding
the sum of laplacian eigenvalues of graphs, The Seventh European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB 2013) CRM Series Volume 16, pp
111-116. Pisa, Italy, 2013.
Last updated: May 1, 2015
Guillem Perarnau, Page 2 of 6
● G. Perarnau. A probabilistic approach to consecutive pattern avoiding in permutations, Actas
de las VIII Jornadas de Matematica Discreta y Algoritmica, Editorial Universidad de Almeria,
2012, ISBN:978-84-15487-13-5.
● D. Mitsche and G. Perarnau. On the treewidth and related parameters of random geometric
graphs, Proceedings of the 29th International Symposium on Theoretical Aspects of Computer
Science (STACS 2012), 408-419, 2012.
● G. Perarnau and O. Serra. Rainbow matchings: existence and counting, Electronic Notes in
Discrete Mathematics, 28 (2011), 711-716. Proc. European Conference on Combinatorics,
Graph Theory and Applications (EUROCOMB 2011), Budapest, Hungary, 2011.
● G. Perarnau and O. Serra. On the treedepth of random graphs,Actas de las VII Jornadas de
Matematica Discreta y Algoritmica, 2010, ISBN:978-84-693-3063-0, pp. 517-528.
● A. Padrol, G. Perarnau, J. Pfeifle and V. Munt´es-Mulero. Overlapping Community Search for
social networks. Proceedings of ICDE 2010, 992-995.
OTHER PUBLICATIONS
● G. Perarnau, Random Combinatorial Structures with low dependencies: existence and enumeration, PhD Thesis, 2013.
● G. Perarnau, Probabilistic methods and coloring problems in graphs, Msc Thesis, 2010.
RESEARCH EXPERIENCE
Talks in Conferences or Workshops
● Acyclic colorings of graph with large girth. Barcelona Mathematical Days 2014. Barcelona
2014.
● Existence of spanning F -free subgraphs with large minimum degree. Siam Conference on Discrete Math. Minneapolis 2014.
● Existence of spanning F -free subgraphs with large minimum degree. Workshop on Graphs and
Algorithms. Toronto 2014.
● Large subgraphs without short cycles. Workshop on Probability and Graphs. Eindhoven 2014.
● Random subgraphs make identification affordable. EUROCOMB 2013. Pisa 2013.
● Random subgraphs make identification affordable. 16th International Conference in Random
Structures and Algorithms. Bordeaux 2013.
● Matchings in Random Biregular Bipartite Graphs. Bordeaux Graph Workshop. Bordeaux
2012.
● Matchings in Random Biregular Bipartite Graphs. STAR Workshop on Random Graphs.
Utrecht 2012.
● Matchings in Random Biregular Bipartite Graphs. 4th PCC. Bedlewo 2012.
● A probabilistic approach to consecutive pattern avoiding in permutations.VIII Jornadas de
Matemtica Discreta y Algor´ıtmica. Almeria 2012.
● A probabilistic approach to consecutive pattern avoiding in permutations.1st Joint Conference
of the Belgian, Royal Spanish and Luxembourg Mathematical Societies. Liege 2012.
● On the treewidth and related parameters of random geometric graphs.STACS 2012, Paris 2012.
Last updated: May 1, 2015
Guillem Perarnau, Page 3 of 6
On the metric dimension of random geometric graphs.BWIC 2011. Bordeaux 2011.
Rainbow matchings of complete bipartite graphs.CSASC 2011. Krems an der Donau 2011.
Rainbow matchings: existence and counting.EUROCOMB 2011 , Budapest, Hungary, 2011.
Rainbow matchings: existence and counting Young Workshop in Arithmetics and Combinatorics, Madrid 2011.
● On the treedepth of random graphs VII Jornadas de Matemtica Discreta y Algor´ıtmica. CastroUrdiales 2010.
● Asymptotic upper bounds on the generalized chromatic number 8th French Combinatorial
Conference. Paris 2010.
● Bounds on the generalized star coloring number for graphs with bounded maximum degree
CSASC 2010. Prague 2010.
●
●
●
●
Seminar talks
● Edge decompositions of graphs with bounded degrees. Groupe de Travail CPU/Axe 3. LaBRI,
Universit´e de Bordeaux 2014.
● Edge decompositions of graphs with bounded degrees. S´eminaire AlGCo. LIRMM, Universit´e
de Montpellier 2014.
● Can Lonely Runner Conjecture be attacked through probability?, Graduate Student Seminar,
McGill University 2014.
● On the diameter of random r-out digraphs, Montreal Probability Group Seminar, McGill
University 2014.
● On the diameter of random r-out digraphs, Discrete Math Seminar, Technische Universiteit
Eindhoven 2014.
● On the diameter of random r-out digraphs, Radboud Universiteit 2014.
● Acyclic colorings of graph with large girth, COMBO Seminar, Darmouth College 2014.
● Existence of spanning F -free subgraphs with large minimum degree, University of Rochester
2014.
● A probabilistic approach to consecutive pattern avoiding in permutations, S´eminaire de GT
probabilit´e et informatique. Universit´e de Bordeaux 2013.
● A probabilistic approach to consecutive pattern avoiding in permutations, S´eminaire de Probabilit´es et Statistiques. Universit´e de Nice 2013.
● A probabilistic approach to consecutive pattern avoiding in permutations, Seminari COMBGRAF. Universitat Polit`ecnica de Catalunya 2012.
● Metric dimension of random geometric graphs, Blackboard Seminar ALBCOM. Universitat
Polit`ecnica de Catalunya 2012.
● Identifying codes for regular graphs, Diskrete Mathematik Seminar. Berlin 2011.
● Dependent random choice. MiniCourse of 4 hours. Universitat Polit`ecnica de Catalunya 2010.
● Identifying codes for regular graphs, Seminari COMBGRAF. Universitat Polit`ecnica de Catalunya
2010.
● Rainbow matchings in complete bipartite graphs, Seminar of LaBRI-Bordeaux 1. Universit´e
de Bordeaux 2011.
Last updated: May 1, 2015
Guillem Perarnau, Page 4 of 6
● On the tree-depth of random graphs, Seminari COMBGRAF. Universitat Polit`ecnica de Catalunya
2010.
Courses and Schools
● Block Course – Towards the Polynomial Freiman-Ruzsa Conjecture, Freie Universit¨at, Berlin
2014.
● Limits of Large Graphs, McGill University, Montreal 2014.
● Positional Games, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach 2013.
● Combinatorial Convexity, Universitat Polit`ecnica de Catalunya,Barcelona 2012.
● Block Course: Extremal Combinatorics in Random Discrete Structures, Freie Universit¨at,
Berlin 2012.
● Eigenvalue Techniques in Graph Theory, Universitat Polit`ecnica de Catalunya, Barcelona
2011.
● Spring School on “Limits of finite graphs”, Max-Planck-Institut f¨
ur Mathematik in den Naturwissenschaften, Leipzig 2011.
● Pre-doc course: Probabilistic and enumerative combinatorics, Methods in Discrete Structures.
Berlin 2010.
● Recent Developments in Largest Graphs and Digraphs with Given Degree and Diameter , Universitat Polit`ecnica de Catalunya, Barcelona 2010.
● Spring school in combinatorics 2010 , Charles University. Borova Lada 2010.
● Advanced Course Polymatroids etcetera: Algorithms and Pretty Theorems, Universitat Polit`ecnica
de Catalunya, Barcelona 2010.
● Graph Minors: Proofs and Algorithms, Universitat Polit`ecnica de Catalunya, Barcelona 2009.
Research stays
Ulm University. Visiting Prof. Dieter Rautenbach. October 2014.
University of Waterloo. Visiting Xavier Perez-Gimenez. May 2013.
University of Rochester. Visiting Giorgis Petridis. May 2013.
Alfr´ed R´enyi Institute of Mathematics. Visiting Prof. G´abor Tardos. May 2013 to June
2013.
● Universit´e de Nice Sophia-Antipolis. Visiting Prof. Dieter Mitsche. January 2013.
● Freie Universit¨at Berlin. Visiting Prof. Tibor Szabo. September 2011 to December 2011.
● LabRi-Universit´e Bordeaux I. Visiting Florent Foucaud. January 2011.
●
●
●
●
TEACHING EXPERIENCE
Lecturer of Graph Theory, 30h, master students of the Master of Advanced Mathematics and
Engineering Mathematics (FME, Universitat Polit`ecnica de Catalunya).
February 2012 - June 2012
Last updated: May 1, 2015
Guillem Perarnau, Page 5 of 6
Lecturer of Probabilitat i Processos Estoc`astics (Probability and Stochastic Processes), 78h,
students of second year in the Bachelor of Information Science and Technology (ETSETB,
Universitat Polit`ecnica de Catalunya).
February 2012 - December 2012
Teaching Assistant for An`alisi Vectorial (Vectorial Analysis), 10h, students of second year in
Telecommunication Engineering (ETSETB, Universitat Polit`ecnica de Catalunya).
February 2010 - June 2010
OTHER ACTIVITIES
● Referee for the international journals Random Structures & Algorithms (RSA), SIAM Journal of Discrete Mathematics (SIDMA), European Journal of Combinatorics (EJC), Discrete
Applied Mathematics (DAM), Discrete Mathematics (DM), Journal of Combinatorics (JoC)
and Theoretical Computer Science (TCS) and for the conferences APPROX-RANDOM 2014,
WG 2014, EUROCOMB 2013 and COCOA 2013.
● Member of the Organizing committee of the ESF-ERCOM-EMS Conference Perspectives in
Discrete Mathematics celebrated on June 2012 in Barcelona.
● Member of the examination committee of PhD students in the Department of Mathematics
at McGill University.
● PhD representative in Department de Matem`atica Aplicada 4 Committee (2011- 2013).
Last updated: May 1, 2015
Guillem Perarnau, Page 6 of 6